Reducibility of 1-D quantum harmonic oscillator with new unbounded oscillatory perturbations

Enlightened by Lemma 1.7 in \cite{LiangLuo2021}, we prove a similar lemma which is based upon oscillatory integrals and Langer's turning point theory. From it we show that the Schr{\"o}dinger equation $${\rm i}\partial_t u = -\partial_x^2 u+x^2 u+\epsilon \langle x\rangle^\mu\sum_{k\in\Lambda}\left(a_k(\omega t)\sin(k|x|^\beta)+b_k(\omega t) \cos(k|x|^\beta)\right) u,\quad u=u(t,x),~x\in\mathbb{R},~ \beta>1,$$ can be reduced in $\mathcal{H}^1(\mathbb{R})$ to an autonomous system for most values of the frequency vector $\omega$, where $\Lambda\subset\mathbb R\setminus\{0\}$, $|\Lambda|<\infty$ and $\langle x\rangle:=\sqrt{1+x^2}$. The functions $a_k(\theta)$ and $b_k(\theta)$ are analytic on $\mathbb T^n_\sigma$ and $\mu\geq 0$ will be chosen according to the value of $\beta$. Comparing with \cite{LiangLuo2021}, the novelty is that the phase functions of oscillatory integral are more degenerate when $\beta>1$.Comment: Journal of Dynamics and Differential Equation

Multi-source excited travelling-wave bowtie antenna based on a meander series of YBCO bicrystal Josephson junctions

Series superconducting Josephson junctions (JJs), as terahertz (THz) mixers, have attracted increasing attentions due to their advantages in solving the saturation problem of superconducting mixers, achieving higher mixing harmonics and higher sensitivity in THz band. However, the normal-state resistances of the series JJs are so low that there exists an impedance mismatch between the coupled antenna and the JJs. In this paper, a meander embedding travelling-wave bowtie antenna is proposed for a series of bicrystal JJs. With this antenna, not only the problem of impedance mismatch can be solved, but also more series JJs can be inserted into the antenna. Five and even seven series JJs in the meander match the proposed antenna well. Furthermore, combined current distribution, far-field radiation patterns and parameter study are investigated in the numerical simulation to analyze this antenna

Mandibular Vertical Growth Deficiency After Botulinum-Induced Hypotrophy of Masticatory Closing Muscles in Juvenile Nonhuman Primates

The purpose of this study was to investigate the relationship between masticatory muscular hypotrophy and mandibular growth in juvenile nonhuman primates (cynolmolgus monkeys, Macaca fasicularis). We hypothesized that botulinum toxin (BTX)-induced neuro-muscular junctional block and its resultant hypotrophy of masticatory muscles would produce mandibular growth disturbances in size and shape. Ten male cynomolgus monkeys were divided into three groups: group I (control; n = 3), group II (unilateral BTX; n = 4), and group III (bilateral BTX; n = 3). The unilateral or bilateral muscular hypotrophy of major masticatory closing muscles was induced by synchronous BTX application to masseter, medial pterygoid, and temporal muscle. Mandibular growth was tracked by linear, angular, area and volume measurements using three-dimensional (3D) computed tomography imaging before BTX treatment and after 3 and 6 months. After unilateral hypotrophy of masticatory muscles in group II, vertical growth deficiency was prominent on the BTX side, with compensatory overgrowth on the control side. The bilateral muscular hypotrophy in group III also showed smaller ramal height and width than that of control (group I) and control side (group II). Moreover, ramal sagittal angles (posterior tilt) increased on the BTX side of both groups II and III, but coronal angles (lateral tilt) did so on the BTX side of group II, resulting in asymmetry. The results confirmed our hypothesis that functional activity of masticatory closing muscles is closely related to mandibular growth in size and shape of juvenile nonhuman primates. In addition, the focused growth disturbances on the ramal height and posterior-lateral tilt suggested the possible role of masticatory closing muscles for ramal vertical and angular growth vector of the mandible

Positive periodic solutions of an epidemic model with seasonality

An SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction Rd number is obtained. Moreover, only the basic reproduction number R0 cannot ensure the existence of the positive equilibrium, which needs additional condition Rd > R1. For the nonautonomous case, by introducing the basic reproduction number defined by the spectral radius, we study the uniform persistence and extinction of the disease. The results show that for the periodic system the basic reproduction number is more accurate than the average reproduction number

SACRB-MAC: A High-Capacity MAC Protocol for Cognitive Radio Sensor Networks in Smart Grid

The Cognitive Radio Sensor Network (CRSN) is considered as a viable solution to enhance various aspects of the electric power grid and to realize a smart grid. However, several challenges for CRSNs are generated due to the harsh wireless environment in a smart grid. As a result, throughput and reliability become critical issues. On the other hand, the spectrum aggregation technique is expected to play an important role in CRSNs in a smart grid. By using spectrum aggregation, the throughput of CRSNs can be improved efficiently, so as to address the unique challenges of CRSNs in a smart grid. In this regard, we proposed Spectrum Aggregation Cognitive Receiver-Based MAC (SACRB-MAC), which employs the spectrum aggregation technique to improve the throughput performance of CRSNs in a smart grid. Moreover, SACRB-MAC is a receiver-based MAC protocol, which can provide a good reliability performance. Analytical and simulation results demonstrate that SACRB-MAC is a promising solution for CRSNs in a smart grid

Adaptive Leakage Protection for Low-Voltage Distribution Systems Based on SSA-BP Neural Network

The fluctuation of normal leakage current has a great influence on the fixed-threshold leakage protector. To address this issue, this paper proposes an adaptive leakage protection method based on the sparrow search algorithm (SSA)-backpropagation (BP) neural network. Based on the analysis of the normal leakage current generation mechanism, this method uses the SSA optimized BP neural network to construct a prediction model of normal leakage current. By dividing the normal leakage range into several intervals and setting the corresponding action threshold, the action threshold of the interval is automatically selected in advance, based on the predicted value of the model, so as to realize the adaptive protection of the leakage current faults. Experiments have proved that the leakage protector can identify the leakage fault more sensitively and increase the ratio of the protector put into operation by predicting the development of normal leakage current and adjusting the protection action threshold in advance

The expanding Earth at present: evidence from temporal gravity field and space-geodetic data

The Earth expansion problem has attracted great interest, and the present study demonstrates that the Earth has been expanding, at least over the recent several decades. Space-geodetic data recorded at stations distributed globally were used (including global positioning system data, very-longbaseline interferometry, satellite laser ranging stations, and stations for Doppler orbitography and radiopositioning integrated by satellite), which covered a period of more than 10 years in the International Terrestrial Reference Frame 2008. A triangular network covering the surface of the Earth was thus constructed based on the spherical Delaunay approach, and average-weighted vertical variations in the Earth surface were estimated. Calculations show that the Earth is expanding at present at a rate of 0.24 ± 0.04 mm/yr. Furthermore, based on the Earth Gravitational Model 2008 and the secular variation rates of the second-degree coefficients estimated by satellite laser ranging and Earth mean-pole data, the principal inertia moments of the Earth (A, B, C) and in particular their temporal variations, were determined: the simple mean value of the three principal inertia moments (i.e., [A+B+C]/3) is gradually increasing. This clearly demonstrates that the Earth has been expanding, at least over the recent decades, and the data show that the Earth is expanding at a rate ranging from 0.17 ± 0.02 mm/yr to 0.21 ± 0.02 mm/yr, which coincides with the space geodetic evidence. Hence, based on both space geodetic observations and gravimetric data, we conclude that the Earth has been expanding at a rate of about 0.2 mm/yr over recent decades